Test 27 - Prismoidal Rule for Earthwork

Question 1 ప్రశ్న 1

Which formula gives the prismoidal volume between two parallel earthwork cross sections a distance L apart, when their areas are A1 and A2 and the actual mid-sectional area is Am?

A V = L(A1 + A2)/2. B V = L(A1 + 4Am + A2)/6. C V = LAm. D V = L(A1 + Am + A2)/3.

Question 2 ప్రశ్న 2

The end areas of an earthwork reach are 12 m2 and 24 m2, and its measured mid-sectional area is 18 m2. If the end sections are 30 m apart, what volume is given by the prismoidal rule?

A 480 m3. B 520 m3. C 540 m3. D 600 m3.

Question 3 ప్రశ్న 3

Two survey cross sections used as the ends of a single prismoidal interval are at chainages 0+080 and 0+140. What is the correct chainage for a cross section located exactly halfway between them?

A 0+110. B 0+100. C 0+120. D 0+140.

Question 4 ప్రశ్న 4

For an earthwork interval of 30 m, the end-sectional areas are 10 m2 and 22 m2 and the measured midpoint area is 15 m2. By how much does the TRAPEZOIDAL estimate exceed the PRISMOIDAL estimate?

A 10 m3. B 15 m3. C 30 m3. D 20 m3.

Question 5 ప్రశ్న 5

An earthwork reach is 30 m long, its end-sectional areas are 10 m2 and 20 m2, and its prismoidal volume is 550 m3. What is the missing mid-sectional area?

A 16 m2. B 20 m2. C 22 m2. D 25 m2.

Question 6 ప్రశ్న 6

The end-sectional areas of an earthwork interval are 8 m2 and 14 m2, and its mid-sectional area is 11 m2. The prismoidal volume is 440 m3. What is the full interval length?

A 40 m. B 30 m. C 50 m. D 60 m.

Question 7 ప్రశ్న 7

Two consecutive earthwork intervals are each 20 m long. Their sectional areas in alignment order are 8 m2 at the first end, 12 m2 at the first midpoint, 16 m2 at the common section, 20 m2 at the second midpoint and 24 m2 at the final end. What is the combined volume by applying the prismoidal rule to EACH interval?

A 600 m3. B 620 m3. C 640 m3. D 720 m3.

Question 8 ప్రశ్న 8

Five consecutive cross sections at equal 20 m spacings have areas of 6, 10, 14, 18 and 22 m2. Using the COMPOSITE PRISMOIDAL (Simpson's one-third) rule over the full four intervals, what is the total volume?

A 1,040 m3. B 1,080 m3. C 1,160 m3. D 1,120 m3.

Question 9 ప్రశ్న 9

Seven consecutive sections have areas of 4, 8, 10, 12, 14, 16 and 20 m2 at equal 15 m spacings. What is their combined volume by the composite prismoidal rule?

A 1,080 m3. B 990 m3. C 1,140 m3. D 1,200 m3.

Question 10 ప్రశ్న 10

One prismoidal reach is 24 m long with end areas 10 m2 and 20 m2 and midpoint area 14 m2. The following reach is 30 m long with end areas 20 m2 and 16 m2 and midpoint area 18 m2. What is the combined volume?

A 844 m3. B 884 m3. C 904 m3. D 944 m3.

Question 11 ప్రశ్న 11

A road embankment has a formation width of 8 m, symmetrical side slopes of 1 horizontal to 1 vertical and level transverse ground. Filling depths vary LINEARLY from 1 m to 3 m across a 30 m reach. What is its prismoidal volume using the end and midpoint cross sections?

A 600 m3. B 620 m3. C 610 m3. D 630 m3.

Question 12 ప్రశ్న 12

An earthwork reach is 24 m long, with end-sectional areas of 9 m2 and 25 m2 and an independently measured midpoint area of 15 m2. By how much does the PRISMOIDAL estimate exceed the MID-SECTIONAL AREA estimate?

A 8 m3. B 12 m3. C 24 m3. D 16 m3.

Question 13 ప్రశ్న 13

A symmetrical embankment has fixed formation width and side slopes of 1.5 horizontal to 1 vertical on level ground. The end depths are 1 m and 3 m, the midpoint depth is their arithmetic mean, and the reach is 24 m long. What is the prismoidal correction, defined as TRAPEZOIDAL volume minus PRISMOIDAL volume?

A 24 m3. B 12 m3. C 18 m3. D 36 m3.

Question 14 ప్రశ్న 14

An embankment on level ground has symmetrical side slopes of 1 horizontal to 1 vertical. Its formation width increases LINEARLY from 6 m to 10 m while the filling depth increases LINEARLY from 1 m to 2 m along a 30 m reach. What is its volume by the prismoidal formula using the midsection obtained from the linearly varying dimensions?

A 425 m3. B 440 m3. C 465 m3. D 480 m3.

Question 15 ప్రశ్న 15

A cutting has a constant formation width of 8 m, with side slopes 1 horizontal to 1 vertical on the left and 2 horizontal to 1 vertical on the right. Cutting depth changes LINEARLY from 1 m to 2 m over a 30 m reach on level transverse ground. What is the prismoidal volume?

A 450 m3. B 460 m3. C 465 m3. D 475 m3.

Question 16 ప్రశ్న 16

A straight-sided pyramid-like earthwork solid has a base cross-sectional area of 36 m2 at one end and tapers to a point at the other end over a length of 30 m. Its midpoint cross-sectional area is 9 m2, consistent with all transverse linear dimensions halving at the midpoint. What volume is obtained by the prismoidal rule?

A 540 m3. B 450 m3. C 300 m3. D 360 m3.

Question 17 ప్రశ్న 17

Under which of the following conditions does the prismoidal formula, considered as Simpson's one-third integration rule, give an EXACT volume when the end and midpoint sectional areas are known accurately?

A The sectional area varies as a polynomial of degree not greater than three with longitudinal distance. B The ground profile is irregular and the section spacing is arbitrarily large. C The two end sections have equal areas regardless of the intervening sectional-area variation. D The midpoint sectional area is always replaced by the arithmetic mean of the two end areas.

Question 18 ప్రశ్న 18

For the DIRECT composite Simpson's one-third form of the prismoidal rule applied to a series of consecutive cross sections, which section arrangement is required without subdividing or treating an interval separately?

A An odd number of equal-length intervals. B An even number of equal-length intervals, producing an odd number of cross sections. C Any number of intervals with arbitrarily unequal spacing. D Only two end cross sections, without any midpoint data.

Question 19 ప్రశ్న 19

Three consecutive sections 15 m apart have areas 10 m2, 16 m2 and 26 m2. The middle section is the exact midpoint of the full 30 m reach. By how much does the COMPOSITE TRAPEZOIDAL volume over the two intervals exceed the PRISMOIDAL volume over the full reach?

A 0 m3. B 5 m3. C 10 m3. D 20 m3.

Question 20 ప్రశ్న 20

At three equally spaced sections 20 m apart, the SOIL excavation areas are 6, 10 and 14 m2, while the ROCK excavation areas are 2, 5 and 8 m2. Using Simpson's one-third form of the prismoidal rule SEPARATELY for each class, what are the soil and rock volumes?

A 600 m3 of soil and zero rock. B 400 m3 of soil and 250 m3 of rock. C 450 m3 of soil and 200 m3 of rock. D 400 m3 of soil and 200 m3 of rock.

Question 21 ప్రశ్న 21

A road alignment changes from CUTTING to FILLING at a verified zero-area section at chainage 0+040. The cutting area at 0+000 is 18 m2 and at midpoint 0+020 is 9 m2. The filling area at midpoint 0+055 is 8 m2 and at 0+070 is 12 m2. What separate cutting and filling volumes are obtained by applying the prismoidal rule to the 40 m cutting reach and the 30 m filling reach?

A 360 m3 cutting and 220 m3 filling. B 360 m3 cutting and 440 m3 filling. C 270 m3 cutting and 220 m3 filling. D 600 m3 cutting and 220 m3 filling.

Question 22 ప్రశ్న 22

Over a 30 m earthwork reach, the true measured sectional areas are 10 m2 at the beginning, 15 m2 at the midpoint and 30 m2 at the end. An estimator incorrectly substitutes the ARITHMETIC MEAN of the two end areas for the midpoint area in the prismoidal formula. How does this change the computed volume?

A It underestimates the correct prismoidal volume by 100 m3. B It overestimates the correct prismoidal volume by 100 m3. C It overestimates the correct prismoidal volume by 50 m3. D It produces no change in volume.

Question 23 ప్రశ్న 23

For an earthwork reach of 30 m, the end-sectional areas are 12 m2 and 18 m2 and the measured midpoint area is 25 m2. How does the PRISMOIDAL volume compare with the TRAPEZOIDAL volume?

A The trapezoidal volume is greater by 200 m3. B The methods both give 450 m3. C The prismoidal volume is greater by 200 m3. D The prismoidal volume is greater by 100 m3.

Question 24 ప్రశ్న 24

Consider three statements. I: The prismoidal formula is exact if sectional area varies quadratically with chainage over the reach. II: The prismoidal and trapezoidal formulas are equal if the measured midpoint area equals the arithmetic mean of the end areas. III: The prismoidal result is always less than the trapezoidal result for any three nonnegative sectional areas. Which option is correct?

A Statements I and II only. B Statements I and III only. C Statements II and III only. D All three statements.

Question 25 ప్రశ్న 25

An earthwork computation contains two consecutive PRISMOIDAL reaches with different lengths. For chainages 0+000 to 0+040, the end areas are 8 m2 and 20 m2 and the midpoint area is 14 m2. For chainages 0+040 to 0+070, the end areas are 20 m2 and 10 m2 and the midpoint area is 16 m2. What is the total prismoidal volume?

A 970 m3. B 1,030 m3. C 1,080 m3. D 1,130 m3.

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